Can a intel i5 7600k 3.8ghz run Fallout 4 High Res packet

I know it's not strictly on-topic, but can I strongly encourage you to consider a Ryzen 5 1600 build instead of an i5.

By the time you get the 7600K, a overclockable motherboard and a cooler you're actually spending a little more than a Ryzen 5 1600 + B350 board. The Ryzen can OC to 3.8ish Ghz on the stock cooler with a cheap mobo. While an overclocked i5 will get better averages in some games, we're already seeing a number of games where the 1% and 0.1% lows are very poor on i5s, indicating that 4 threads are sometimes not enough. That trend is likely to continue.

It's probably worth starting a different thread with your budget and goals for your build. You should get some great suggestions. You can ask the i5 vs Ryzen 5 question. I suspect you'll see most people recommending Ryzen.

Anyway - to your original question the recommended requirements for that texture pack are absurd, a 6 core 12 thread 5820K + a GTX 1080. HardOCP did a review on a 6700K and found it was playable on mid-range GPUs. So the 1070 should have no problem. I can't find any CPU benchmarks, though the 6700K is clearly sufficient. Whether the i5 can handle it well I can't really say. I think it will be playable, at least. The Ryzen 5 is much more comparable to a 5820K, so if the game does actually scale up to 12 threads, Ryzen is going to handle that better in theory. But I don't the game or the hardware myself, and without reputable benchmarks, it's all speculation.

Some fallout 4 bench's I ran across.

http://www.pcgamer.com/the-amd-ryzen-7-review/5/
https://www.bit-tech.net/hardware/2017/04/11/amd-ryzen-5-1600x-review/5
http://www.gamersnexus.net/game-bench/2182-fallout-4-cpu-benchmark-huge-performance-difference

According to that gamersnexus link, the 7600k stock had similar min fps to the r5 1600x oc'd and higher average fps by a good lead in bf1. TW warhammer, same thing. Watchdogs 2, same thing. Metro last light the ryzen had a clear advantage finally. Ashes, they were almost identical. Maybe based on price but otherwise it seems odd to say the i5 has a 'fading grasp' when it performed better on 3/5 games listed and tied with ryzen on one of them.

As for the high res pack, high res is a gpu load. No gpu was listed in the current system to hold over until upgrading to the 1070. If relying on the integrated graphics until the 1070 purchase then it's almost a no brainer, the intel chips have igpu's and ryzen doesn't. You'll need a gpu for ryzen to do anything with it. The integrated graphics on the intel chips are functional for a variety of things, but not for gaming really and a high res pack would only make matters worse. The cpu performance ryzen vs intel isn't going to be determined based on a resolution upgrade (higher quality in game images), that's the gpu's job.

Others aren't wrong, some games generally do perform better thank to hyper threading on an i7, bf1 being one of them. Many benchmarks are difficult to achieve for bf1 since most people play in multiplayer and most benchmarks aren't done in that environment. It's difficult to repeat the data and get confirmed results because each run through isn't perfectly the same as the last. Also any improvements made via game updates or ryzen bios updates may be missed, it's a lot of work benchmarking games. They can't go back and retest each and every game every time a change is made which may or may not affect fps.

Hardocp's review of the high res pack. Notice the concentration on gpu performance, not cpu.
https://www.hardocp.com/article/2017/02/12/fallout_4_high_resolution_texture_pack_review/13